Part BCSIR NET December 2023adjusted-r-squared

Adjusted r squared

Consider $Y = α + β x + ε$ with $E (ε) = 0$ . From 10 observations the OLS fit is ŷ = 1.5 + 0.8x. Suppose $\sum (y_{i} -$ ȳ $)^{2} = 5$ and $\sum (x_{i} - \overset{x}{ˉ})^{2} = 6$ . The adjusted $R^{2} ($ to two decimals) equals

A.0.74
B.0.83
C.0.77
D.0.84

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The trap it tests

Execution slip

The idea was right. The computation was not.

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Related counterexample: OLS is the BLUE in every linear model

Adjusted r squared

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